"An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.1 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 260 engines and the mean pressure was 4.2 pounds/square inch. Assume the standard deviation is known to be 0.9. A level of significance of 0.02 will be used. Determine the decision rule. Enter the decision rule."

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jtellezd jtellezd · Answer 1 · 2020-08-07T22:22:38+02:00

Answer:

H₀ is accepted, we don´t have evidence to claim valves produces more than 4,1 pounds/square inch

Step-by-step explanation:

Normal Distribution

Population mean μ₀ = 4.1

Population standard deviation σ = 0,9

Sample size n = 260

Sample mean μ = 4,2

Level of significance 0,02 α = 0,02 form z-table we find z score

z(c) = 2,05 (critical value)

Test hypothesis

Null hypothesis H₀ μ = μ₀

Alternative hypothesis Hₐ μ > μ₀

Is a one tail-test ( to the right. Values have a mean over the population mean)

z(s) = ( μ - μ₀ )/ σ /√n

z(s) = 4,2 - 4,1 / 0,9/√260

z(s) = 0,1 *16,1245 / 0,9

z(s) = 1,7916

To compare z(s) and z(c)

z(s) < z(c)

Then z(s) is in the acceptance region, we accept H₀